A categorification of the colored Jones polynomial at a root of unity
Abstract
There is a $p$differential on the triplygraded KhovanovRozansky homology of knots and links over a field of positive characteristic $p$ that gives rise to an invariant in the homotopy category finitedimensional $p$complexes. A differential on triplygraded homology discovered by Cautis is compatible with the $p$differential structure. As a consequence we get a categorification of the colored Jones polynomial evaluated at a $2p$th root of unity.
 Publication:

arXiv eprints
 Pub Date:
 November 2021
 arXiv:
 arXiv:2111.13195
 Bibcode:
 2021arXiv211113195Q
 Keywords:

 Mathematics  Quantum Algebra;
 Mathematics  Geometric Topology;
 Mathematics  Representation Theory;
 57M27;
 18G99
 EPrint:
 72 pages, many figures. Comments welcome!